Question: Rewrite as a simplified fraction. ${3.4\overline{2} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 342.2222...\\ 10x &= 34.2222...\end{align*}}$ Subtracting the two equations, we have: ${90x = 308}$ ${x = \dfrac{308}{90}} $ ${x = \dfrac{154}{45}} \text{or} {3 \dfrac{19}{45}}$